If $x \triangleleft y = 4x^{2}-y^{2}$ and $x \bigtriangledown y = x+6y$, find $-3 \triangleleft (-6 \bigtriangledown 1)$.
Solution: First, find $-6 \bigtriangledown 1$ $ -6 \bigtriangledown 1 = -6+(6)(1)$ $ \hphantom{-6 \bigtriangledown 1} = 0$ Now, find $-3 \triangleleft 0$ $ -3 \triangleleft 0 = 4(-3)^{2}-0^{2}$ $ \hphantom{-3 \triangleleft 0} = 36$.